This book was written twenty years ago, but we are leaving it unchanged - not because little has happened to the subject, but because so much has happened that any change would require very major rewriting. On the other hand, no other book on the subject seems to have appeared and we hope this paperback edition will be of some use to a younger generation - if not for another twenty years, at least until someone else has the patience to write a new book. Although we have added no new material we have corrected some misprints. We have added new references only where they correct actual errors. We are grateful to Drs. G. Feinberg, M. Inokuti, Y. Kim, and A. Petermann for pointing out errors.

Nearly all of this book is taken from an article prepared for a volume of the Encyclopedia of Physics. This article, in turn, is partly based on Dr. Norbert Rosenzweig's translation of an older article on the same subject, written by one of us (H.A.B.) about 25 years ago for the Geiger-Scheel Handbuch der Physik. To the article written last year we have added some Addenda and Errata. These Addenda and Errata refer back to some of the 79 sections of the main text and contain some misprint corrections, additional references and some notes.

Units.- I. The Hydrogen Atom Without External Fields.- a) Nonrelativistic theory.- 1. Separation of Schrödinger's equation in spherical polar coordinates. Angularly dependent eigenfunctions and the angular momentum matrix.- 2. Derivation of Balmer's formula.- 3. The radial eigenfunctions of the discrete spectrum.- 4. The eigenfunctions of the continuous spectrum.- 5. Motion of the nucleus.- 6. Separation of Schrödinger's equation in parabolic coordinates.- 7. Methods for the continuous spectrum for a general central potential.- 8. Wave functions in momentum space. Discrete spectrum.- 9. Wave functions in momentum space. Continuous spectrum.- b) Dirac theory.- 10. General properties of the Dirac theory.- 11. Angular momentum.- 12. Pauli theory of the spin-electron.- 13. Pauli theory for a central potential.- 14. The exact solution of the Dirac equation.- 15. Dirac equation. Continuous spectrum.- 16. The Dirac equation in momentum space.- 17. The fine structure formula.- c) Radiative and other corrections.- 18. Radiative corrections. S-matrix theory.- 19. Radiative corrections. Bound states.- 20. Corrections for nuclear motion and structure.- 21. Fine structure and the Lamb shift.- 22. Hyperfine structure splitting.- 23. The fine structure of positronium.- II. The Helium Atom without External Fields.- a) Nonrelativistic theory.- 24. The Schrödinger equation for helium (symmetry).- 25. Discussion of variation and perturbation methods.- 26. Level scheme of helium.- 27. Survey of approximations to be used.- 28. First order Heisenberg's method (excited states).- 29. Polarization for excited states.- 30. Fock's method (excited S-states).- 31. Hartree's method.- 32. Ritz variation method (helium ground state).- 33. Ground state of helium-like ions with arbitrary Z.- 34. The negative hydrogen ion.- 35. Variation method for excited states.- 36. Miscellaneous calculations I.- 37. Motion of the nucleus.- b) Relativistic theory.- 38. Discussion of the Breit equation.- 39. The Pauli approximation (low Z).- 40. Fine structure splitting of helium.- 41. Relativistc corrections for the ground state.- 42. Breit equation without external field.- 43. Treatment for large Z.- 44. Hyperfine structure.- III. Atoms in External Fields.- a) Zeeman effect.- 45. Zeeman effect for a single-electron atom.- 46. Dependence on magnetic field strength.- 47. Some corrections to the Zeeman effect.- 48. Extension to many-electron atoms.- 49. Comparison with precision experiments.- 50. The diamagnetism of helium.- b) Stark effect in hydrogen.- 51. Linear Stark effect.- 52. The quadratic Stark effect.- 53. Stark effect for strong fields.- 54. Ionization by the electric field. Quenching of the lines in the Stark effect.- 55. Stark effect of the fine structure of hydrogen.- c) Stark effect in helium.- 56. The Stark effect for weak fields.- 57. Dependence on field strength.- 58. The dielectric constant of helium.- IV. Interaction with Radiation.- a) Discrete spectrum.- 59. General formulas.- 60. Selection rules for orbital and magnetic quantum numbers.- 61. Sum rules.- 62. Proof of the sum rules.- 63. The transition probabilities for hydrogen in polar coordinates.- 64. Intensity of fine structure lines.- 65. Intensities in parabolic coordinates (Stark effect).- 66. Higher multipole radiation.- 67. Lifetimes of excited states in hydrogen.- 68. Alkali and X-ray spectra.- b) The photoeffect.- 69. General survey.- 70. The Born approximation.- 71. The absorption coefficient without retardation.- 72. Angular distribution and retardation.- 73. Relativistic effects.- 74. The optical region.- 75. Recombination.- c) Bremsstrahlung.- 76. General survey.- 77. Nonrelativistic Born approximation.- 78. Calculations for low energies.- 79. Relativistic effects.- Appendix on spherical harmonics.- Addenda and errata.- Further addenda and errata.- Author index.- Index of Tables.